Magnetometric resistivity tomography using chaos polynomial expansion

Abstract

SUMMARY We present an inversion algorithm to reconstruct the spatial distribution of the electrical conductivity from the analysis of magnetometric resistivity (MMR) data acquired at the ground surface. We first review the theoretical background of MMR connecting the generation of a magnetic field in response to the injection of a low-frequency current source and sink in the ground given a known distribution of electrical conductivity in the subsurface of the Earth. The forward modelling is based on sequentially solving the Poisson equation for the electrical potential distribution and the magnetostatic (Biot and Savart) equation for the magnetic field. Then, we introduce a Gauss–Newton inversion algorithm in which the logarithm of the electrical conductivity field is parametrized by using the chaos polynomial expansion in order to reduce the number of model parameters. To illustrate how the method works, the algorithm is successfully applied on four synthetic models with 3-D heterogeneous distribution of the electrical conductivity. Finally, we apply our algorithm to a field case study in which seepage was known to be occurring along an embankment of a headrace channel to a power station.